Liverpool were the better team and extended their unbeaten run in the Premier League to eight matches, but Brendan Rodgers knows they should have won on his return to west Wales, and were again undermined by their shortcomings in front of goal. If Luis Suárez does not score for them nobody does, and the Uruguayan had an off day here.

Liverpool had the lion's share of the chances and felt they were unjustly denied a winner just before half-time, when José Enrique had the ball in net but was judged offside by what was a debatable decision. They were unlucky, too, when Raheem Sterling' shot shivered the crossbar.

Michael Laudrup thought his charges deserved a point but admitted it may not have looked that way "from the outside". He was happy with the Swans' performance – and how they dealt with Suárez and Steven Gerrard – as well as the extension of a sequence during which they have lost only one in seven in the league.

Both teams are starting to get it together under new management. Laudrup had a hard act to follow when Rodgers decamped to Liverpool in the summer and there were murmurs of discontent from the dressing room at the end of September, after three successive defeats in the league. Disgruntled tongues have been stilled, however, with some improved results of late – notably the 3-1 win at Liverpool in the Capital One Cup and last week's 2-1 victory at Newcastle.

For Rodgers, too, all has not been sweetness and light since he left his west Wales comfort zone to succeed Kenny Dalglish at Anfield. A 3-0 defeat at West Brom on opening day and five games without a win was hardly the start he needed in the league but the green shoots of recovery are apparent in an improved run.

They are still a work in progress, of course, their most obvious weakness the lack of a goalscorer to share the burden with Suárez. The Uruguayan has weighed in with 10 in 13 league matches but nobody else has contributed more than one. Young Sterling, newly elevated to the England squad, has one in 19 appearances in all competitions.

"It's something we need to improve", Rodgers said after the game. "We've had 18 shots at goal, nine of them on target and we haven't scored. We need someone apart from Suárez to round off a lot of the good play we saw today."

The first question was answered early. What sort of reception would Rodgers get on his return to the Liberty for the first time? He deserved an appreciative round of applause after establishing the Swans in the Premier League but neutrality was the best the crowd could manage. The Ulsterman said: "It was an emotional occasion for me because I've seen so many people who shared great moments in my life. I was really looking forward to it and it was a wonderful atmosphere and a terrific game."

Swansea were quickly into their pleasing passing style, fostered by Rodgers and Roberto Martínez before him, and the first goal attempt of note saw a crisp drive from Wayne Routledge, on the right, bring a plunging save from Pepe Reina at the foot of his near post.

For Liverpool, Glen Johnson, who was outstanding, had a shot deflected over by Gerhard Tremmel after a pass and move incursion that called to mind Liverpool in their halcyon days.

Pablo Hernández threatened with a curling strike from 20 yards but Liverpool were closest to a goal when Sterling, from 12 yards, thumped a shot against the bar and Enrique had the ball in the net, but from a debatably offside position. "We were unfortunate there", Rodgers said. "I thought it was a goal."

Suárez, with a powerful, low shot brought an improvised save from Tremmel, using his body, early in the second half as Liverpool resumed the offensive. Getting nowhere and seeking an injection of pace, Laudrup sent on Nathan Dyer and the flyer soon raced past Stewart Downing, who was playing at left-back, into the penalty area, only to be foiled, and injured, by Reina's charge from his goalline.

As both players received treatment, the crowd chorused: "You know he's a diver, put Suárez in goal." Instead, Suárez burst free, through the middle but, after exchanging passes with Sterling, shot straight at Tremmel.

Hernández, with a free-kick from 25 yards, tested Reina to his left and Jonjo Shelvey, on as substitute, threatened to win it at the death with a thunderous shot, but inaccuracy when it mattered most forced them to settle for a point apiece.